Let's talk about the balloon first because it provides a pretty good model for the expanding universe.

It's true that if you draw a big circle then it will quickly expand as you blow into the balloon. Actually, the apparent speed with which two of the points on the circle in a distance $D$ of each other would move relative to each other will be $v = H_0 D$ where $H_0$ is the speed the balloon itself is expanding. This simple relation is known as Hubble's law and $H_0$ is the famous Hubble constant. The moral of this story is that the expansion effect is dependent on the distance between objects and really only apparent for the space-time on the biggest scales.

Still, this is only part of the full picture because even on small distances objects should expand (just slower). Let us consider galaxies for the moment. According to wikipedia, $H_0 \approx 70\, {\rm km \cdot s^{-1} \cdot {Mpc}^-1}$ so for Milky way which has a diameter of $D \approx 30\, {\rm kPc}$ this would give $v \approx 2\,{\rm km \cdot s^{-1}}$. You can see that the effect is not terribly big but the given enough time, our galaxy should grow. But it doesn't.

To understand why, we have to remember that space expansion isn't the only important thing that happens in our universe. There are other forces like electromagnetism. But most importantly, we have forgotten about good old Newtonian gravity that holds big massive objects together.

You see, when equations of space-time expansion are derived, nothing of the above is taken into account because all of it is negligible on the macroscopic scale. One assumes that universe is a homogenous fluid where microscopic fluid particles are the size of the galaxies (it takes some getting used to to think about galaxies as being microscopic). So it shouldn't be surprising that this model doesn't tell us anything about the stability of galaxies; not to mention planets, houses or tables. And conversely, when investigating stability of objects you don't really need to account for space-time expansion unless you get to the scale of galaxies and even there the effect isn't that big.

Let's talk about the balloon first because it provides a pretty good model for the expanding universe.

It's true that if you draw a big circle then it will quickly expand as you blow into the balloon. Actually, the apparent speed with which two of the points on the circle in a distance $D$ of each other would move relative to each other will be $v = H_0 D$ where $H_0$ is the speed the balloon itself is expanding. This simple relation is known as Hubble's law and $H_0$ is the famous Hubble constant. The moral of this story is that the expansion effect is dependent on the distance between objects and really only apparent for the space-time on the biggest scales.

Still, this is only part of the full picture because even on small distances objects should expand (just slower). Let us consider galaxies for the moment. According to wikipedia, $H_0 \approx 70\, {\rm km \cdot s^{-1} \cdot {Mpc}^{-1}}$ so for Milky way which has a diameter of $D \approx 30\, {\rm kPc}$ this would give $v \approx 2\,{\rm km \cdot s^{-1}}$. You can see that the effect is not terribly big but the given enough time, our galaxy should grow. But it doesn't.

To understand why, we have to remember that space expansion isn't the only important thing that happens in our universe. There are other forces like electromagnetism. But most importantly, we have forgotten about good old Newtonian gravity that holds big massive objects together.

You see, when equations of space-time expansion are derived, nothing of the above is taken into account because all of it is negligible on the macroscopic scale. One assumes that universe is a homogenous fluid where microscopic fluid particles are the size of the galaxies (it takes some getting used to to think about galaxies as being microscopic). So it shouldn't be surprising that this model doesn't tell us anything about the stability of galaxies; not to mention planets, houses or tables. And conversely, when investigating stability of objects you don't really need to account for space-time expansion unless you get to the scale of galaxies and even there the effect isn't that big.